To prove Theorem REF  REF , it might be possible to use the mean oscillation approach in [1]}. However [1]} fails when \((a_j)_j\)  has infinite nonzero terms. This is critical if one wants to prove the Besov and Triebel-Lizorkin boundedness of Seeley's operator (see Remark REF ) using such method. The authors do not know what the correct modification of [1]} is.
